Electric Classes
Charging batteries time-consuming.
Need to buy half dozen pinions for gearing options.
Clean and easier to race using grid starts.
Bodies don't need cooling holes.
Costly to run anything other than 540 - need access to lathe. ($200- $300). More club members now have lathes now, so only a small fee will get you a reco comm.
Costly to run hot modifieds - need good batteries ( $100+ea.)
Easy to hone driving skills. Can concentrate on handling settings. Cars are generally less heavy and lower CofG than nitro cars and consequently handle better.
Diversity of motor classes can be a problem (Situation improving with international popularity of 27 turn rebuildable 'stock' motors).

Nitro Classes
Chassis gets very dirty.
Reliability problems, compounded by long finals with pit-stops.
Engine and 2 speed tuning extra dimension to hobby.
Hard on tyres.
Plenty of cheap power.
Great crowd pleaser. Sound great. Often considered more realistic.

Costs that apply to both;
Need a range of good tyres (expensive).
Poor driving with overpowered cars can cause grief. Seems to be more a problem in nitro classes, where new-starters have the power without the handling to match.
Need spare crystals to race at club days.
Open top-spec racing in electric and nitro is not well supported at club level due to $$$ required to get into it..

So, which is more expensive to get into?
A tricky question - the answer depends on how seriously you end up getting into racing? If you stick to entry level racing like 540 (silver can) electric racing or pullstart nitro racing, then nitro is definitely the more expensive class to run in due to outlay and maintenance costs.
However, if you get into modified electric racing then you can easily spend more money than a fairly high-end nitro package. It is hoped that brushless electric motors will make high powered electric racing more affordable in the near future. The choice is yours…

Other common questions for people starting out in electric racing;

Stick or Side-by-side battery packs?
Stick less efficient at high current load (hot modified motors).
Stick cannot be individually discharged (balance tray recommended for matched packs)
Stick packs more foolproof against shorting. Safer for juniors or beginner racers.
Not all chassis can take stick, but becoming more common (eg. TC3, Yokomo MR/SD, HPI Pro3/Pro4, Tamiya TA04)
Warning! Some of the cheaper stick packs are CRAP and soon die under normal racing use. Only buy well known cells such as Sanyo, Panasonic and Gold Peak.

NiMH vs NiCd?
NiMH producing way more capacity/run-time than NiCd now. Only really an issue for modified motors.
Early NiMH had less punch. Latest HV/SMH/UMH generation as good if not more punch than NiCd.
NiCd are more robust to peak detect charging. Pretty well indestructable as they dont get ballistically hot when fast charged and post-trickle charging them actually helps them cool down.
NiMH doesn't require cycling as often as NiCd, some recommend against deep discharge with NiMH.

Charging Practices?
Always discharge your pack fully using a resistor or light bulb until the pack 'dumps' then disconnect the load. If you don't do this, then after a few months you will notice the pack seems to deliver less run-time and doesnt feel very punchy at all! This is often refered to as memory effect.
A pack can be recharged once it has cooled to room temp. This can take a couple of hours! Charging a pack that is not rested will cause it to vent its guts as it overpressurises, effectively permanently damaging the cells performance.
NiMH have the advantage of being fairly immune to memory so you dont have to dump the pack before you reuse it and this means the same pack can be re-used again later in the race meet.
NiCd's also respond well to being deeply discharged slowly overnight on a tray or using a single 30 Ohm 5W resistor. Although it doesnt need to be done every time, if you haven't done it in a while you may notice a slight increase in punch due to this. NiMH are advised against deep discharge altogether though some still reckon its the way to go!
Charging is done at the fastest rate your charger can provide without melting your battery in the process! The idea is that a pack charged at 6A will feel punchier than if charged at 3A. This is marginal and the truth is the convenience of a faster charge time is the main reason we charge at high rates.
Overnight trickle charging however is definitely less punchy than a fast charge, and if you find the logistics easier to charge the day before race day then make sure to repeak the pack just before you race as the pack will have lost its edge sitting around for too many hours.
A warm freshly charged pack is the optimum power platform for electric racing. period.