Building your own team buys you the most control. The engineers learn your domain over months and years, and this context remains inside the company. The catch is time and rigidity: filling a senior role takes months, getting someone productive takes several more weeks, and the cost keeps running through the quiet quarters.
Project outsourcing means someone else is accountable for shipping: the provider staffs the roles, the partner manages the day-to-day work, and the provider carries the staffing risk. This works well when the outcome can be described and your side has an available product owner. It works badly when nobody on your side owns the product, as a vendor is not able to fill that gap for you.
Team extension falls in the middle: you add engineers but keep the management yourself. It moves quickly — a suitable engineer can join far sooner than a new hire nginx developers — and the commitment ends when the work does. The catch is that your own leads have to have time for code review and planning. If that capacity is missing, you end up paying for effort with no owner.
Most of the time, custom software development stack these models are combined. A common pattern puts the critical decisions and the core system inside the company, while an outside vendor takes on the parts that are bounded and specifiable. The principle is simple enough: keep what differentiates you, and contract out what is well understood.
A few questions usually settle it. Start here: is the system a core competitive asset, or a cost centre? Next: over what horizon will you need this capacity — a quarter or a decade? Finally: who answers the phone at two in the morning when it breaks? Answer those honestly and the appropriate option becomes obvious.