You wrote:
The House Intelligence Committee just voted to release a memo drafted by Chairman Devin Nunes and other Republicans which discusses alleged misconduct by the FBI in the Trump-Russia investigation.
All media reports I've seen claim the memo was drafted by Devin Nunes and committee staff.
Also, here's how Reuters characterizes the memo:
Two sources familiar with the memo said it accuses the FBI and the Justice Department of abusing their authority in asking a Foreign Intelligence Surveillance Court judge to approve a request to extend an eavesdropping operation on Carter Page, an adviser to Trump’s 2016 campaign.
The memo charges that the FBI and the Justice Department based the request on a dossier compiled by a former British spy hired to dig up negative information on Trump by a research firm partially financed by the Democratic National Committee and Hillary Clinton’s presidential campaign.
source: Reuters
You wrote:
Democrats on the committee claim that this memo is misleading, and they drafted their own memo which was based on the same intelligence that the Nunes memo was based on...
You should provide a reference that supports your claim that the Democrats' memo is based on "the same intelligence that Nunes" used.
You wrote:
... except they claim their memo paints a more accurate picture of what the intelligence actually says.
Again, a reference would be useful.
You wrote:
Republicans on the House Intelligence Committee voted to release the Nunes memo, but voted against releasing the Democratic memo. My question is, have Chairman Nunes or any other Republicans on the committee publicly discussed why they voted against releasing the Democratic memo?
Republicans are saying they need time to read the Democrats' memo.
Representative Mike Conaway, a senior committee Republican, said Republicans voted against releasing the Democrats’ memo because the House of Representatives had not had a chance to read it. He said the committee agreed to let House members read it and would consider making it public after that.
source: Reuters
Also, maybe Republicans want all eyes on their memo without any distractions for the moment.
[House Intelligence Committee Ranking Member Adam ] Schiff said
Republicans said they might consider [releasing the Democrats' memo]
in another week. So depending on when the Nunes memo becomes public,
it could dominate the discussion in Washington and TV airwaves for
several days before Democrats' counterpoint is unveiled.
source: NPR
Also consider this:
Your question, more precisely, may be: Why did all Republicans on the House Intelligence Committee vote against releasing the Democratic memo?
You can then ask: Why did all Democrats on the House Intelligence Committee vote against releasing the Republican memo?
One can extrapolate, based on the vote tallies alone, that partisan political interests, in particular, the upcoming mid-term elections, are also an influence driving each member's vote.
More information: https://intelligence.house.gov/