When I was at Letourneau, the main difference between the BSWE and BSWET programs was math related. BSWE's went through Calculus III and Differential Equations, and BSWET's went through Calculus II with an introduction to differential equations. The Welding Engineering classes back then were identical for both majors. The other courses were divided between engineering and technology courses, with engineers being taught more theory, and technology majors being taught more practical and hands on skills. WE's were taught how to design complex electrical circuits, and technology grads were taught how to program and troubleshoot automation and electrical control systems.
To be honest, there is not a lot of high level math required in the everyday welding industry. I have seen complex models (some which run on supercomputers) used to predict phase transformations, weld size, and metallurgical reactions; in nearly every case, they were only able to conjure a "best guess" result. Advanced welding theory does have its place, but at the end of the day, it is the practical skills that are most in demand by employers who simply want to get the job done. A solid understanding of Welding QA testing methods is mandatory for both majors.
If you get an education with a solid foundation in the basics of welding theory, you will still be a great fit for many employers. My employers in the past always had metallurgists on staff, some with PhD’s even. So, I have worked with a wide range of people in my career to date. And, some of the best welding engineers of all time had no degree at all. Check out George Linnert of AWS fame who wrote Welding Metallurgy Vol's 1 and 2.
Very few states have a PE certification for WE's. Most WE's that do get a PE get it in Mechanical Engineering. I have only seen one WE job description (out of thousands) in the last 33 years that required a PE certification. And, don't forget, a BSWET could still take the AWS Certified Welding Engineer exam, which might carry more weight than a PE cert. But, I will be quick to admit that a BSWE would have a greater chance of passing the exams, and some projects like welding design for bridges and buildings might mandate possession of a PE cert. But, I had a job offer right out of school to do welding design for offshore drilling rigs. I made an A in my Design of Welded Structures Course, and that was all they cared about. All my calculations would have been checked by a PE, and I would have been checking his calculations!
OBEWAN is spot on with the differences between technology degrees and the BSWE degrees. I'm a OSU WE and a good deal of my time in school was spent learning theory with some valuable, but not really extensive, hands on time. I compensated for that during and when I got out by seeking out hands on type positions so I could gain some real world expertise to go with my theory. I'll also echo the sentiments about high level math not really being used every day. Welding is a very empirical field, so most of what is done in industry is to weld a sample and test it. Today, I wear every hat I'm handed. Sometimes I'm a glorified technician who wears steel toes, jeans, and a hoodie to work while doing procedure development for critical mechanized GTAW applications. Other times I'm giving presentations to customers, either on my results or pitching a job. Other times I'm reviewing my client's specifications/procedures and offering feedback. Regardless of which path you go, make sure the school you attend offers typing and public speaking classes (assuming you don't already have those skills). Those have been, hands down, the two most value able classes for me. The rest of the information I learned in school I can look up in a book on my shelf, but I can't fake communications skills.
As for the math part, I might add that you should get at least one course in statistics. More and more employers are moving to the use of Six Sigma methods, and you will need a stats background to pass the cert test. Stats might be the most valuable math course as far as my career goes.
But, nowadays, computers do all the heavy lifting. I have used the MiniTab program at more than one employer to do some advanced stats calculations.
And, stats will help you win many a fight and even get you out of trouble. On one project, I read some R&D reports on LASER aluminum welding before going to the job interview. The reports all stated a 6% cracking probability for a certain alloy and only 2% for other alloys that were more "weldable".
Well, guess what? I took on the project and had to fight an ongoing 5% crack reject rate for the aluminum laser welds. The employer demanded 100% yields, which is a virtual impossibility from a statistical standpoint.
If you are lucky, your employers will invite you to sit in on design review meetings to either accept or reject the materials selections for new products. That is what is known these days as "Design for Six Sigma", or DFSS. Unfortunately, not everyone does it yet. But, at least if you make your case known, and put it in writing, you might get off the hook if an insurmountable problem comes up and a manager is pounding on you to "fix" it.
As far as I know, the state of Ohio was the last state to offer a PE exam specifically for welding. I beleve this was discontinued a year or 2 ago. It is my understanding that for the NCEES (the National Council of Examiners for Engineering and Surveying) to re-approve a PE exam for welding, at least 10 states must participate. Probably will never happen
A mechanical engineer friend recently received his PE stamp from the state of Texas AND! AWS Welding Engineers certification. He says the AWS was much harder. And the CWI test was a walk in the park compared to those two.