Unix timestamp vs timestamptz index performance
To answer your basic question: No. timestamptz is stored as 64 bit integer quantity internally (same as int8). An index on it performs identically to one on  a bigint (int8) column - when used correctly. Related:

Ignoring time zones altogether in Rails and PostgreSQL

If in doubt, go with timestamptz. It's built for the purpose. The only argument in favor of Unix timestamps would be that you already have them and use them elsewhere.
As for the query plan added later. Consider a multicolumn index like bbaird suggested. See:

Multicolumn index and performance

You might rewrite the table physically to help this particular query. CLUSTER takes an exclusive lock. To deal with concurrent write load consider pg_rewrite or pg_squeeze. Either requires excess storage and time for a big table. See:

Configuring PostgreSQL for read performance