I'm not an expert on the subject, but poking around a little, it turns out that several people have talked about this. As per your question clarification, I'm addressing how the Jack Broughton gloves have impacted the sport.
First, and foremost, padded gloves make it much safer to punch an opponent with greater force, and in harder angular areas such as the head. It distributes the impact force over a larger surface area, mitigating both increased punching force and the risk of your opponents body exerting an equal-and-opposite force over a small area against your knuckles. Boxers can, and do, punch with more force than before, and unlike a bare-knuckle sport such as Lethwei boxers punch at the head with no fear that their opponent will set their head to injure the incoming fist.
Second, the gloves are weighted. Much like wielding a weapon, it increases your striking force, but also leads to increased fatigue because you're moving an additional pound or so of force with your arms. This requires a greater utilization of the entire body to throw the punch rather than just the arms or the upper body. The increased fatigue also increases the efficacy of the "rope-a-dope" technique of letting an opponent wear themselves out with repeated punches, dodging or absorbing the blocks to minimize damage for your opponent's fatigue.
Thumb positioning in the fist
This is a debated one, but some boxers claim that modern boxing gloves teach "mitten thumb" due to the padding over the thumb preventing the boxer from properly tucking their thumb over the first 2-3 knuckles and instead encouraging the boxer to keep his thumb tucked over the top of his hand where it's more likely to catch and break on a missed hit. There's been at least one patent to address the issue.
Restriction of grappling and gouging techniques
Lastly, the padded gloves were arguably introduced as much to prevent grappling as they were to prevent injury from punching to either party. The puffy nature of the modern Broughton glove made it significantly more difficult, if not impossible, to make use of techniques such as eye-gouges, fish-hooking, and grappling, all common techniques in bare-knuckle matches.