I was looking over the heads that came with my RR (the engine was apart when I bought it) and noticed the heads are mismatched one is a 906 and the other a 346.
What are the differences between these heads? I had never heard of the 346 before.
Can you mix these?
Should I look for both and run which ever I find first or just look for a 906?

The 346 is the head that came after the 906. It is functionally equivalent.
Same combustion chamber
Same cc
Same intake and exhaust flanges.
Same flow
Slightly different intake port configuration, if one was porting
Neither one has induction hardened valve seats (It is possible that a 1973 model year 346 head could have induction hardened exhaust seats.)

What you do depends entirely onyour budget, your wish to restore and your vehicle year.

If you are a restorer, you want to find a head which matches the year. The 906 was a 1968 to 1970 head. The 346 was a 1971 - 1973 head. You can look up Chrysler casting numbers online.

If you have the budget and don't wish to restore, there are much better heads out there, the 440Source Stealth and the Edelbrock E-street are the two lowest priced worthwhile heads.

If you have any notion about the stock iron heads for high performance, give it up. It'll cost more to have them ported and rebuilt than it'll cost to buy the above aluminum heads.

Before you put a nickel into either head, get a firm written quote from the shop, then check your options.

If you "just want an iron head so I can drive the car" then look for a set of 452s, the latest bigblock castings that have induction hardened valve seats and have the same lousy flow and combustion chamber as any of the 1968-and-up bigblock heads.

R.

PS: I have edited the content to correct the model years. I hate to be inaccurate.

The reality is, these heads are satisfactory in four aspects:
1. They cover the cylinders.
2. They connect to the intake and exhaust manifolds.
3. They position the sparkplugs.
4. They hold the valves and springs.

They fail in that they flow only marginally better than a stock 340 head, and they have a lousy open combustion chamber that aggravates detonation and requires a lot of ignition lead to get to best power.

If you are in the mood to do some reading http://www.moparts.org/Tech/Archive/bb/62.html http://www.moparts.org/Tech/Archive/bb/40.html http://www.moparts.org/Tech/Archive/bb/42.html

they are nearly identical & you will not notice any difference tho it does go against the grain to have an identical pair of parts on an engine but they ain't the same. If you want to read up on em access Dulcichs' Mopar Muscle porting articles which impressed me as the final word on porting iron BB heads. As said I would not sink any serious money into them. iron is heavy/likely need milled to be flat (decks and intake face)/open chambers give no quench potential/452's can be cracked/early ones (915/906) need a flow bench/experience to properly port em & I would stay with OE valve sizes on early ones/use the MP templates. If I was to invest in em I would find a pair of crack free 452's and go with 2.14/1.81 valves & unshroud the chamber (valve) ends and cut the MP templates larger out of the laminated sheet. Always always always practice porting on a junk head bufore starting on a good set. With the good alum heads available and how much it will cost to do the iron ones I would pass unless they are ready to go & even then I would just port with the MP templates on the stock valves (if you can still get them) (alot of gain to be had).

I believe that the 346 head was first used in the 1971 production motors As already pointed out, no noticeable differences in performance though

I know a guy that bought a 71 R/T Charger brand new and the car was delivered that way.

Basically the same head as everyone has said but there is one visual, external difference. There is one or two extra casting ribs next to the freeze plug at the ends of the head. Maybe someone someday might ask why you have two different heads but if that doesn't matter to you, use em.