Ok, an attempt for an input now.
Regarding BVR-
Su-27/33- Advantage of the Su-27/33 is the big number of missiles onboard. Detection range and look-down capabilites are also good. That gives to the Flanker room for more option than the MiG for example- you detect him further he can. Also- the 27/33 is a flying fuel tank- great range and you don't have to worry about flying burners that much, again compared to the mig. Also it has the missiles with biggest range in the game (human controlled a/c). Disadvantage- no active missiles, no TWS shots, you need to go STT and always compromise your launch, so in multiple target engagement it's more dificult than the F-15. It's deadliest weapon in LO is the 27ET because it gives no warning. The Su-33 has an advantage of having two extra long range missiles.
F-15- powerful radar, great detection and lock range, great look down abilities. With fuel tanks it's range is even bigger than Flanker's and carrying fuel tanks doesn't block any weapon hard point like the wingtanks of the MiG. It can carry up to 8 active missiles which could be launched in TWS mode thus giving warning only after the missile goes active (pitbull). IFF is partically modeled and for that the F-15 is "famous" with the plane with most teamkills. You can IFF but you must be careful. Disadvatage- lack of passive sensors (EOS) and small chance of surprise. So when engaging you always have yourself compromised.
MiG-29S- deadliest plane in LO- small size, harder to detect, hard to spot visualy. It carries the deadliest missiles in LO- 27ET and 77. Weapon system is the same as of Su-27/33's with less powerful radar but fire-and-forget ability because of the R-77. Great acceleration rate and seems to be the only plane in LO with relatively exact drag at supersonic speed. With all other planes you can't go faster than Mach 1.2-1.3 with payload. The missiles are like airbrakes. Biggest disadvantage- short range, even with 1 tank. But because of the great acceleration you may stay out of burner and still engage or break. If you take wingtanks too then you can't take 27ER/ET missiles. This is other weak point of the MiG- 6 missiles in total with only 4 medium range. So two things are cruicial for that plane- fuel and missile management.
Another important moment IMO is that flying all planes will greatly improve the skills. By knowing the advantages of one plane you can predict what to expect when you face it. I was flying russian planes only in BVR but from about 1-2 months I started trying the F-15 and I liked it. It made me better understand the BVR when I looked from the other side.
For dogfight-
Flanker or Eagle- no doubt about that. The MiG is so castrated in that area that it's not even funny. You can do it but you must go out of the standarts. There are people in my squad that can write Ph.D. thesis on that so I'll let them speak. The F-15 has better TWR than Su-27 and sustained turn rate too at higher speed. But watch out your pull- Eagle's pilot blacks out sooner than Flanker's.
I like flying all planes and I can say I became equaly good (or bad, depending on the point of view :P- if the bottle is half full of halp empty) in any of them both in BVR and guns. Learning all of them equally made me enjoy LO even more.