SSB and SF2 are very different games. Their strategies revolve around very different things.
SF2 is about space control and effectively trapping the player in a corner and depleting their health bar. Every move has a counter and the play is relied heavily on knowing distances of hit-boxes.
SSB is about building the percentile damage of one player and trying to knock him off the stage (and if you're a bastard, keep him off using very unfriendly tactics). This play is about quick dodges, and knowing which moves will knock a player off the stage effectively.
The lack of health bar changes things significantly, but I feel the biggest difference is the chance for a 'comeback'.
This is what separates good fighting games from the bad, in my opinion.
SF2 has chipping damage, and no countering/dodging system save for trying to attack the other person back before they can hit you. SSB has the dodge roll, and 'side-step' feature alongside the fact that you can't actually die via straight damage so the battles can rage on if you can evade long enough.
I find a 'counter' system like the 'parry' system they have in SF3: 3rd Strike is brilliant. It gives a skilled player a chance to come back from the most epic of beatings. Another great system is the 'guard break' system from Soul Calibur. Simple, yet effective.
This timing system allows players to have a much greater chance at a 'comeback' which turns dull matches into an explosion of awesome. So while Smash Bros. doesn't have this type of counter, it atleast has a 'dodge' system which SF2 lacks. I love my Street Fighter, but I just love Smash Bros. for the simple fun of it rather than studying a frickin' hit box chart. Low level play = awesome for both. High level is ridiculous for both.
Overall: Smash Bros.