Every carrier is going to have areas where they have poor and excellent coverage and consequently areas with fast and slow data speeds, its just going to vary by geographic location (so you won't necessarily be going from fast to slow). I would recommend talking to your friends/family/co-workers that have Sprint in your area and see how they like their service. Technically speaking, both Sprint and Verizon use the same technology for their 3G coverage (CDMA EV-DO) so its going to be things like available bandwidth, number of users, distance from the tower, etc that are going to affect your 3G data speed.
For 4G, Verizon uses LTE while Sprint currently uses WiMax. Verizon's 4G LTE is technically faster but its been my experience than unless you are using a hotspot or laptop to utilize their 4G network, you aren't going to experience much (if any) difference at all in speed vs Sprint for tasks on your phone like casual web browsing, streaming music/video, checking email, etc. I believe this is primarily due to the phone itself being a bottleneck in that its processor/graphics chipset/etc (as advanced as they are) simply can't process the data fast enough to the point where you are going to see a usable difference between (for example) 8mbps on Sprint's network and 15mbps on Verizon's network. In my experience, both offer more speed than your phone can utilize for the types of tasks I listed above. If you plan to use your phone as a hotspot though in areas where Verizon has LTE coverage, well then you may see a difference of 1-3 seconds when doing things like web browsing on a laptop, etc. Again though, I would try to speak with people in your area who own the Evo 3D or the Bionic and see what their impressions are of their carrier's data speeds. Every city/location is different and it would not be accurate to say that one carrier is always or mostly always going to have faster data speeds than another (especially for two carriers like Sprint and Verizon that use the same 3G technology and that both have advanced 4G networks).