Short: Depends.
If you develop/test stuff with lot of parallel I/O - real LA like TLA7xxx are gold. They provide complex state machines timing support, segmented memory and module ACQ can be clocked and triggered by your DUT device,all of which makes any DSO with "LA" functionality nothing but a toy. I managed to get AA4 module to capture and decode about 600MHz DDR bus, but best to stay under 400MHz for ease of use. Today's modern BB4 module offers 1.4GHz BW, but cost like a fancy car unless you get in right place in right time.
There do not support usual slow serial comms out of the box, that's not what they are designed for. With some cursing and coding you can write own "support module" to add decode though. I've covered decode modules and flow on
my site about I2C and SPI decoder. For fast stuff, like DDR decode there are suppliers that provide the HW and SW plugins, but that's not cheap.
To you questions.
1. Yes, you can make software decoders (within module limits for BW/depth), but not pain free process.
2. FSM support is great, but TLA app can be picky working with long captures (4M+ samples with lots of channels). However if you need such deep memory - you configuring your event capture wrong
3. 715 can support most of newer modules like 7AA/7AC4, while 704 is ancient box, limited to old modules. Tek software will not work until you are on right OS. I'd suggest to stay at least with 715. Only 7012/7016 supports modern modules like 7BB4 and PCIe modules.
7AA4 does not have analog inputs, those BNCs are mux outputs. Very useful thing when used together with Tektronix scope (google iView).
TLA app can show analog signal on screen, aligned to your digital waveform, but need external scope to digitize data. TLA is not a realtime device either.
There are DSO modules like 7E2/7E4 but those are very limited.
4. BB4 can do 1.4GHz BW. There is extension function to get small sample capture but at much higher speed - Tek calls it magnivu. That can provide equiv 8GHz BW on AA4 module and 50GHz on BB4 hardare.
And using TLA standalone on it's own small screen and UI is pita, so all those older units useable only with remote LAN control. You can install TLA application on your usual windows machine, and play with "demo" analyzer to see what it can do. it runs simulator TLA7016 when no Tek HW detected.
But it can be picky on modern machines with lots of DRAM (8GB+) and 64-bit OS, e.g.:
Except special DSO modules for TLA, none of the modules have ADC to digitize any analog signals. So..
but buying TLA LA unit with TLA7AA4 module, i will have both professional humongous channels LA, and professional GHz grade DSO... no?
No, you get just a TLA. You need iView set (NI GPIB dongle and BNC-BNC cable set for triggering) and Tektronix scope like TDSxxxx or DPO/MDO/DSAxxxx to get analog data into TLA view:
Also do not forget, you can get TLA mainframe and 7AA4 for cheap, but your main expense will be always in probes and fixtures. 7Ax4/7BB4 use Mictor impedance controlled ports , so you can't whack your usual 100mil pitch cable into them and expect anything good.
If you really interested, I can give you poor condition (but working) TLA714+7AA4 and custom probe for cost of shipping, since I've upgraded to TLA7012+7BB4+7AC4 while ago.