I dunno exactly how you guys are getting your numbers, but I got SE as stronger. So... math.
The formula is [averageDamageOfCannon*numberOfBullets*1000/speed] for DPS. SE adds an average of 21% per bullet (140*.15)
DPS
None: 2202.9% =3.8*4*1000/690
SI: 2303.03% =3.8*4*1000/660
SE: 2324.64% =4.01*4*1000/690
Both: 2430.3% =4.01*4*1000/660
DPM
None: 132173.91% =3.8*4*60000/690
SI: 138181.82% =3.8*4*60000/660
SE: 139478.26% =4.01*4*60000/690
Both: 145818.18% =4.01*4*60000/660
Realistically, it'd probably be best to buff yourself with SE before you go in, then do SI the rest of the time. If you wanna be lazy though, SE is stronger. Also, no Bullseye in any of the above calcs. If you want to know what it would be with Bullseye, then just multiply the % in bold by 1.2. It doesn't change their relationship with one another at all, though.
The formula is [averageDamageOfCannon*numberOfBullets*1000/speed] for DPS. SE adds an average of 21% per bullet (140*.15)
DPS
None: 2202.9% =3.8*4*1000/690
SI: 2303.03% =3.8*4*1000/660
SE: 2324.64% =4.01*4*1000/690
Both: 2430.3% =4.01*4*1000/660
DPM
None: 132173.91% =3.8*4*60000/690
SI: 138181.82% =3.8*4*60000/660
SE: 139478.26% =4.01*4*60000/690
Both: 145818.18% =4.01*4*60000/660
Realistically, it'd probably be best to buff yourself with SE before you go in, then do SI the rest of the time. If you wanna be lazy though, SE is stronger. Also, no Bullseye in any of the above calcs. If you want to know what it would be with Bullseye, then just multiply the % in bold by 1.2. It doesn't change their relationship with one another at all, though.