/u/grampipon

Your impressions are correct, although the question of whether the Swedish army was truly much more modern is still debated today. To understand all this, let's take a step back and see how warfare was evolving at that point.

From Breitenfeld to Munich

The year 1630 must have seemed a great moment for the Catholic-Imperial side. Wallenstein and Tilly's forces reigned supreme, with no competing Protestant power in the conflict. Emperor Ferdinand II promulgated the Edict of Restitution, with the intention of recovering secularized Catholic fiefs back to the situation agreed on during the 1555 Peace of Augsburg. But internally, the situation wasn't exactly rosy, for Wallenstein had many critics, some jealous of his successes and some unhappy that in 1629 he made little significant engagement against the Protestants. Thus, in September 1630 the Emperor dismissed Wallenstein, who some observed to have expressed relief, for he knew his army was difficult to maintain, what with the limits of bureaucracy, logistics, and revenue.

Now, enter the Swedes ...

Following the (first) Battle of Breitenfeld in September 1631, the army of the Catholic League led by Count of Tilly was in tatters and was desperately re-building. They were the only nontrivial Catholic Imperial army still standing; the Emperor had dismissed Wallenstein in fall 1630 following which he retired. The Swedish victory in Breitenfeld thus gave two advantages. First, they forced the Imperial army on a desperate defensive. Second, they forced erstwhile neutral parties into alliance with the Swedes, as they had no alternative.

The Catholic League army of Tilly desperately recruited and entrenched themselves in winter 1631-32. While the Swedes, surprisingly, were highly mobile. They had significant stock, fodder, transports, so they started to move southwards to the surprise of the Imperials. This forced Tilly to move in November to block their path toward Munich or Vienna. At the same time, Pappenheim's mounted reiters moved north-west to harass the Swedish rear. To quote an observer, Tilly was,

'Wholly perplexed and seemingly cast down, wholly irresolute in council, knows not how to save himself, abandons one proposal after another, decides nothing, sees only great difficulties and dangers—but has no idea how to overcome them.'

By this point Tilly had about 22,000 soldiers and Gustavus about 37,000. Tilly couldn't decide whether he should seek safety or seek to put himself in Gustavus' path. Tilly ended up deciding to seek a position that could allow him to obtain both safety and strategic blockade, but during his movement, his army was surprised by Gustavus' unexpected crossing of the Lech river at Rain, resulting in annihilation of Tilly's army and mortal wounding of its commander.

Gustavus' army thus rampaged Bavaria with no opposing army to challenge it; Gustavus and Frederick V entered Munich in a victory parade in May 1632. In desperation, the Emperor sought help from the Spanish army of Flanders, but they were facing a resurgent Dutch advance toward the Rhine and thus unable to send an expeditionary force southwards.

Wallenstein returns

In desperation, the Emperor recalled Wallenstein in April 1632, to raise a completely new army. This he did in a mere three months, even if he had to sell commissions to bandits, criminals, and other undesirables, to the consternation of his veterans. Importantly, everybody knew that Wallenstein's army may have quantity but it likely did not have quality. Thus Wallenstein, after securing a base in Bohemia and Prague, astutely sought safety and held out in Alta Veste just outside Nuremberg starting in August 1632, which was being besieged by Gustavus. Essentially, Wallenstein chose to shadow Gustavus' army and force it to attack his entrenched position, rather than seeking an open conflict nor attempt a direct relief of the siege. Clashes of arms through skirmishes were inevitable, as much as inundation of the countryside by two hungry armies.

'For three months we were besieged by our enemies; for four months we were eaten out by our friends'

Failing to invest Nuremberg and suffering losses due to hunger and disease, in September 1632 Gustavus had to retreat toward the north-west while Wallenstein shortly after went north-east toward Saxony, in order to plunder those territories while Gustavus sought safety in his lines of communication. In this, Wallenstein had some success as he was able to take Leipzig in November 1632. He also started to absorb remnants of the Catholic League's army.

Wallenstein's tactical mistake

By that time, winter was fast approaching, so Wallenstein was convinced that campaigning season was over. He detached Pappenheim's contingent to the northwest to support the Imperial position in Koln -- a very important possession on the Rhine -- and in November 14 1632 he sent commands to disperse his army to winter quarters. This was common practice at the time, to disperse a large army to spread the burden of its maintenance over a large area and large population. But this time, Gustavus happened to be starting his aggressive move toward Wallenstein at the same time, having received news that Pappenheim had been despatched. The Swedish army embarked on a rapid march toward Wallenstein. So the very next day, Wallenstein had to recall his order and Pappenheim's detachment.

Battle of Lutzen and aftermath

As we know, both sides displayed brilliance during the Battle of Lutzen, and two key commanders perished during battle: Gustavus and Pappenheim. The Imperials had to retreat from the field of battle, and stop their advance toward Saxony. At the same time, the Protestant side lost a leader who could impose his will on all allies. From this point on, much more diplomacy and negotiation was needed to preserve Protestant unity.

And of course, personally for Wallenstein, this led to what was perceived to be a much more timid and cautious command of the army, while he seemed to invest more and more in making himself a leader for negotiations.

For the above, I replied on Parker's Thirty Years' War in addition to Schiller's Thirty Years' War.