What RA will be generated if intruder traffic is at our level in TCAS II?
The TCAS algorithms are specified in RTCA/DO-185B (not freely available).
In case of an encounter at same altitude with a non TCAS equipped aircraft, assuming that neither climb nor descent are inhibited, the TCAS will produce a descent advisory (part 2, sec. 2.2.4.1.2.1.5 - sense selection).
This is a consequence of the somewhat subtle signs used in the specification (&lt;= for descend, &gt; for climb).

A non mode-S intruder will broadcast altitude with a 100ft resolution, and a TCAS equipped aircraft will normally use barometric altitude with 25 ft resolution, so the two aircraft do not need to be at exactly the same altitude - in the worst case, a difference of up to 62 ft will be interpreted as &quot;same altitude&quot;.

There are also provisions for climb and/or descent inhibits. In particular descend RAs are inhibited below 1000ft radio altitude.
Climb RAs are inhibited when the aircraft performance are not compatible with a 1500 fpm climb (for example, one engine out). The exact mechanism through which this information is provided to the TCAS computer is aircraft dependent.
In your case of same-altitude encounter, if descend RAs are inhibited, a climb RA will be generated.

EDIT
As requested, more clarification.
A simplified description of RTCA-DO185B initial sense selection follows. This description assumes that the intruder is not TCAS equipped, and that the firmness (confidence in intruder altitude and position) is sufficiently high.
First, choose the direction (climb or descent) that will produce the highest separation at CPA (see below).
If equal, select descent (see 3.52 Noncrossing_Biased_Climb and 3.53 Noncrossing_Biased_Descent).
Denote this direction with D

If a RA in the D direction does not result in a crossing (see below), then issue an RA in the D direction.
Otherwise, if the opposite direction still provides at least ALIM separation, then issue an RA in the direction opposite to D.
Otherwise, issue an RA in the D direction.


Separation: The TCAS algorithm models a RA response as follows:

5 seconds of reaction time (pilot maintains current airspeed and rate-of-climb)
A segment with a constant acceleration of 8 ft/s^2 in the direction of the RA
A final segment at constant rate of climb (usually + or - 1500 fpm).

To select the sense, the TCAS algorithm considers:

Distance from intruder
Time derivative of distance from intruder (closure rate)
Time derivative of the closure rate
Ownship altitude and rate of climb
Intruder altitude and rate of climb

With these 5 parameters, the vertical separation at the CPA (Closest Point of Approach) can be computed.
In this scenario, the relative altitude is zero, and the rate of climb of both intruder and ownship are 0. Due to the symmetry of the model, the separation will be the same for both climb and descent.

Crossing
Crossing is defined as either:

A climb RA, with ownship at least 100 ft below the intruder
A descent RA, with ownship at least 100 ft above the intruder

In this scenario, ownship and intruder altitude are equal, so neither direction will result in a crossing RA.