Not being familiar with the characterisitcs of the filler metal or the intent of its design, at first glance I see:
A .12 C filler being used on L Grades?
There could be a sensitization problem here, even though I am assuming the N means nitrogen and could get the Cr instead of the C.
But are nitrides better than carbides?
A filler being used with nominal Cr lower than the BM?
There could be an issue with oxidizing services.

I would say than in order to answer your question you would have to have some idea of the service intended.
I would also contact the manufacturer and get more info on the design purpose of the material.

Hi Steelman7018!

Why not use 308L to weld the two members of 304L? Is there a specific application that would warrant the use of this filler electrode which is made by whom, and would you by any chance know the chemical composition of this filler electrode designated as: E16-25MoN-15? According to this web link it states:

http://www.china-welding.com.cn/pr6.htm

"Welding of low and medium alloy steels which is in state of quench dissimilar steels, big rigid structures and compound heat hardening steels. Such as 30CrMnSi." and in the link , the electrode is written as "E16-25MoN-16" instead of ending with the number 15. Hmmm... ;) This link is to an MSN Word .doc which lists the electrode as you posted it originally:

http://yfhc.mysteel.com.cn/Mild%20steel%20welding%20electrode.doc

And it states the use for:

"Low hydrogen Cr16Ni25Mo6 pure authentic (I believe they meant to write Austenitic instead of Authentic :) ) electrode with titanium calcium coating.It should be connected with negative polarity on DC in all positions.Usage is the same to A502."

C           Si          Mn         Cr          Ni         Mo            others
≤0.12%   ≤0.9%  ≤2.5%  14-18%   22-27%  5-7%   Cu≤0.5%    N≥0.1% 
Note: I see a very high amount of carbon right off the bat when compared to a low carbon grade such as a E308L.

And this is what A502 is:

"Cr16Ni25Mo6 pure authentic (More than likely Austenitic instead of Authentic! ;) ) electrode with titanium calcium coating.It can weld on both DC and AC.Used to weld low alloy steel,heterogeneity steel in quenching condition ,as well as the relevent refractory steel."

My advice is to use a 308L electrode unless it's specifically required under the contract specifications and if it is, I would at the very least, find out the what & why justification for using this electrode instead  of E308L and since I do not know the exact chemical composition of the Base/parent 304L stainless steel, I would also check that out also via the MTR (Mill Test Report). This Electrode designation "E16-25MoN-15" I believe is a British standard MMA (Manual metal Arc) designation (SMAW) but then again, I may be incorrect in my observation since I'm no expert in those standards. ;)

Respectfully,
Henry