Yes, the Trump Tower meeting is vastly different than normal opposition research.
1. The meeting might be a direct violation of campaign finance law
Not everyone agrees, but there is an argument to be made that this was an offer from a foreign entity to contribute "something of value", which could violate US campaign finance law:
“The Trump campaign invited them to come. It was a proposition that was offered, and it was accepted,” Bauer said, referring to the exchange of messages between Trump Jr. and music publicist Rob Goldstone that set up the meeting itself — an email exchange that indicated the offer was “part of Russia and its government’s support for Mr. Trump.”
“The law prohibits Americans from soliciting foreign nationals’ assistance,” he added. “The solicitation provision is very broad. You don’t have to specifically say, ‘I really would like you to do X’; you could indicate, since they’ve already said they want to help you out, that you’re open for business. That you actually want their support.”
In contrast, a campaign hiring a firm to research Trump's overseas business interests isn't a violation:
“Paying a foreign national fair market value for opposition research is generally not illegal,” Noble wrote. “It is considered a commercial transaction, which is not a contribution.” Clinton’s campaign had paid Fusion GPS directly; it’s a campaign expenditure, not a campaign contribution. Since it’s not a contribution, the FEC allows it.
2. The material (supposedly) discussed was obtained via illegal hacking
12 Russian hackers have been indicted for hacking the DNC and the Clinton campaign.
If (as is generally believed) that this hacked material is the "dirt" on Clinton that was offered by the Russians during this meeting, and if Mueller has evidence (or testimony) that members of the Trump campaign were aware of or cooperating with the Russians "in furtherance of" these crimes, then it is possible that Trump campaign officials could face federal conspiracy charges. From the same article as above:
Further, and importantly, the law prohibits any American from aiding any of the above efforts. We noted last week that “collusion” can be another word for “conspiracy,” and that those aiding a Russian effort to provide illegal assistance or soliciting that assistance could be held criminally liable.
Your question asks whether Trump is right that "most people would have taken that meeting", if getting oppo research from anywhere and everywhere possible is "done all the time in politics". I'd suggest the answer is no: in September 2000, Gore's campaign received an anonymous package containing info about Bush's debate prep. Their immediate reaction was to call the FBI.
There is no allegation that anything in the "Steele Dossier" was obtained illegally.
3. The secrecy and lies about this meeting indicate they knew it was wrong.
If this was "no big deal", why has everyone involved lied about it for years?
If this was "no big deal", why would Trump Jr. lie to Congress under oath about whether his father knew about the meeting?
And when portions of the story did come out, why did their story continue to change a dozen times or more?
The obvious answer (in my opinion), is simply that they knew it was wrong, and knew if it got out that it would kill their chance to get elected.
Legal analysts describe this as a "consciousness of guilt", others even suggest this is "direct evidence of crimes".
(In my opinion, this record of obfuscation means we should continue to be highly skeptical of the Trump campaign's current claims about the meeting: that it came to nothing, that there was no agreement, that Trump wasn't aware of it, etc.)
In contrast, it wouldn't strike anyone as unusual for a campaign to hire a firm well known for performing opposition research.
4. This meeting wasn't about "adoptions", it was about using adoptions as leverage for dropping sanctions.
A 2012 US Law called the "Magnitsky Act" froze money in the US that belonged to Russians implicated in human rights abuses, including the 2009 murder of anti-corruption activist Sergei Magnitsky. In retaliation, Russia blocked international adoptions of Russian orphans:
Since that time, Russia’s efforts to reverse the Magnitsky Act and lift other sanctions, like those that the United States imposed after Russia’s invasion of Crimea, have been a constant through-line of its foreign policy. They remain a critical priority for Mr. Putin, who sees the sanctions as one part of a broader effort by Western governments to undermine his presidency.
Ms. Veselnitskaya, the Russian lawyer who attended the Trump Tower meeting, has claimed in interviews that Donald Trump Jr. agreed to reconsider these sanctions if Trump is elected.
Proof of a "quid pro quo" along these lines would be (to put it mildly) a pretty big deal.
5. The country involved is a (past and current) adversary of the US.
It is one thing to believe that we can work, carefully and cautiously, towards a gradually improved relationship with Russia.
It's a different thing altogether to knowingly cooperate with a hostile foreign power currently involved in an active campaign to disrupt our election.
