Be careful about reading too much into the "300 mA" or "1A", as the current spec on transistors can be very misleading: I've seen people assume that because a bipolar (or MOSFET, or diode, or LED...) says "5A" in big letters on the datasheet, that they can put 5A through it under any condition - smoke usually ensues!
Think of the current rating more as a way to compare transistors, not as an absolute metric. Having blown up plenty of power devices myself, and hopefully learned something from it, the things that actually matter are:
1. How easily the transistor can get rid of the heat: this is more about the package than anything else. I don't know how much power you're planning on allowing your output transistors to dissipate, but I'm going to make up some numbers here, just for an example. Let's say the amplifier is putting out 1W at 50% efficiency: this means it's dissipating 1W too, mostly in the output transistors, 0.5W for each one. Now looking at the datasheet for the SOT-23 parts, it shows 357 C/W junction-to-ambient thermal resistance - that means that the temperature of the transistor's die is going to be 0.5W*357 C/W=179 C above ambient temperature...if the ambient air temperature around the transistor is maybe 60 C inside a box on a hot summer day, that bit of silicon (rated only to 150 C, by the way) is going to be at 239 C! Instant explosion.
On the other hand, if you use the other transistor, because the package has a big metal tab its junction-to-ambient thermal resistance is about half of the other one (192 C/W), which means that the temperature rise above ambient will be only half as big. That's only some of the benefit: the metal tab also provides a good place to conduct even more heat away either into an external heatsink, or to a copper area on the PCB as a cheap heatsink. Check out the thermal conductivity list on page 6, and notice that the thermal resistance (junction to ambient) drops from 192->125->93 C/W as you go from no extra copper -> 1 cm^2 extra copper -> 6 cm^2 extra copper.
Again, most of this is applicable to pretty much any transistor in a SOT-23 package vs. a SOT-223 package, not just these two particular part numbers. There's some variation between manufacturers, etc. but one package type is usually pretty consistent. Be careful about footnotes and test conditions: the BCP56 datasheet has very good info about thermal resistance, while some "too good to be true" thermal resistance numbers I've seen on other datasheets for some tiny SOT-323 package turn out to be only when using a special ceramic (high-thermal-conductivity) PCB with 4 cm^2 pads on every pin, once you dig into the footnotes.
2. Other effects like "secondary breakdown" (essentially non-uniform conductivity causing hot spots which cause thermal runaway) on bipolar transistors: check the device's "safe operating area" (SOA) diagram for this limit.
Apologies if you know all this already: just looked like a common misunderstanding was about to happen, and hoped to maybe save some unnecessary smoke
