I think if your sole criteria for improvement is bass, you'll be disappointed with the E4s. I've spent a lot of time with these two phones (the E3s were my primaries for about 8 months, and the E4s were for close to a year), and I'd say that the E4s have a smidgen more bass in the lowest frequencies, but noticeably less in the higher-bass and lower-mid frequencies. I prefer the bass on the E4s, quality-wise, but again, it's not a huge huge difference. The real reason to upgrade from E3s to E4s is vocals and mid-treble, both of which are massively better on the E4s than E3s.
If you're looking for bowl-you-over bass, skip to the E500s. I'd say that, on a scale of 1 to 10, the bass of the E3s is probably a 3, the E4s is probably a 4, and the E500s is about a 9.5. Huge huge huge bass. Too much maybe.